Question

Two small spheres each of mass m and charge q are tied from the same rigid support with the help of silk threads of length L. They make angle $\theta$ with the vertical as shown in the figure.
If length L is decreased then angle $\theta$ with the vertical :

• A. increases
• B. decreases
• C. unaffected
• D. cannot say

Answer 1

The correct option is A increases

At equilibrium, $Tcos\theta =mg$ ............$\left(1\right)$

and $Tsin\theta =F_C$

$Tsin\theta =\frac{K{q}^2}{(2Lsin\theta {)}^2}$ where $K=\frac{1}{4\pi {ϵ}_o}$

$Tsin\theta =\frac{K{q}^2}{4L^{2}si{n}^2\theta }$

From $\left(1\right)$ $\frac{mg}{cos\theta }sin\theta$$=\frac{K{q}^2}{4L^{2}si{n}^2\theta }$

$⟹tan\theta$ $si{n}^2\theta$ $=\frac{K{q}^2}{4L^{2}mg}$

Thus when $L$ decreases, then $\theta$ increases.